Is there any way or Extention in Magento to handle multiple payment gateways like for credit card transaction one payment gateway, for EMI transaction another payment gateway and for net banking another gateway in below screenshot way
You can offer multiple ways for users to checkout. You could offer the option to checkout via credit cards that would be processed through, for example, Authorize.net while also offering the option for users to checkout via Google Checkout or PayPal Express (amongst other options).
Additionally, there's no reason why you couldn't roll your own through a custom module.
If you're talking about actually having two different payment gateways setup at the same time, you would need to do that on a per-store configuration basis. There are some examples out there.